http://rsos.royalsocietypublishing.org/cgi/content/short/5/11/180746?rss=1
A weakly nonlinear stability analysis of shear flows based on amplitude expansion is re-examined. While it has been known that the condition required to define the coefficients of the resulting Stuart–Landau series representing the nonlinear temporal evolution of the most amplified Fourier component of a disturbance is not unique, we show that it can be formulated in a flexible generic form that incorporates different conditions used by various authors previously. The new formulation is interpreted from the point of view of low-dimensional projection of a full solution of a problem onto the space spanned by the basic flow vector and the eigenvector of the linearized problem. It is rigorously proven that the generalized condition formulated in this work reduces to a standard solvability condition at the critical point, where the basic flow first becomes unstable with respect to infinitesimal disturbances, and that it results in a well-posed problem for the determination of coefficients of Stuart–Landau series both at the critical point and a finite distance away from it. On a practical side, the generalized condition reported here enables one to choose the projection in such a way that the resulting low-dimensional approximate solution emphasizes specific physical features of interest via selecting the appropriate projection weight matrix without changing the overall asymptotic expansion procedure.
]]>2018-11-14T00:05:38-08:00info:doi/10.1098/rsos.180746hwp:master-id:royopensci;rsos.1807462018-11-14Physics511180746180746http://rsos.royalsocietypublishing.org/cgi/content/short/5/10/181122?rss=1
Modern political interaction is characterized by strong partisanship and a lack of interest in information sharing and agreement across party lines. It remains largely unclear how such partisan echo chambers arise and how they coevolve with opinion formation. Here, we explore the emergence of these structures through the lens of coevolutionary games. In our model, the payoff of an individual is determined jointly by the magnitude of their opinion, their degree of conformity with their social neighbours and the benefit of having social connections. Each individual can simultaneously adjust their opinion and the weights of their social connections. We present and validate the conditions for the emergence of partisan echo chambers, characterizing the transition from cohesive communities with a consensus to divisive networks with splitting opinions. Moreover, we apply our model to voting records of the US House of Representatives over a timespan of decades to understand the influence of underlying psychological and social factors on increasing partisanship in recent years. Our work helps elucidate how the division of today has come to be and how cohesion and unity could otherwise be attained on a variety of political and social issues.
]]>2018-10-24T00:05:33-07:00info:doi/10.1098/rsos.181122hwp:master-id:royopensci;rsos.1811222018-10-24Physics510181122181122http://rsos.royalsocietypublishing.org/cgi/content/short/5/10/180863?rss=1
Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical–mechanical model of urban transformations, exemplified for Greater Sydney, and derive a thermodynamic description highlighting critical regimes. We consider urban dynamics at two time scales: fast dynamics for the distribution of population and income, modelled via the maximum entropy principle, and slower dynamics evolving the urban structure under spatially distributed competition. We identify phase transitions between dispersed and polycentric phases, induced by varying the social disposition—a factor balancing the suburbs’ attractiveness—in contrast with the travel impedance. Using the Fisher information, we identify critical thresholds and quantify the thermodynamic cost of urban transformation, as the minimal work required to vary the underlying parameter. Finally, we introduce the notion of thermodynamic efficiency of urban transformation, as the ratio of the order gained during a change to the amount of required work, showing that this measure is maximized at criticality.
]]>2018-10-17T00:05:33-07:00info:doi/10.1098/rsos.180863hwp:master-id:royopensci;rsos.1808632018-10-17Physics510180863180863http://rsos.royalsocietypublishing.org/cgi/content/short/5/10/180692?rss=1
The d’Alembertian = 0 has the solution = f(v)/r, where f is a function of a null coordinate v, and this allows creation of a divergent singularity out of nothing. In scalar-Einstein theory a similar situation arises both for the scalar field and also for curvature invariants such as the Ricci scalar. Here what happens in canonical quantum gravity is investigated. Two minispace Hamiltonian systems are set up: extrapolation and approximation of these indicates that the quantum mechanical wave function can be finite at the origin.
]]>2018-10-10T00:05:17-07:00info:doi/10.1098/rsos.180692hwp:master-id:royopensci;rsos.1806922018-10-10Physics510180692180692http://rsos.royalsocietypublishing.org/cgi/content/short/5/10/180208?rss=1
The variational problem of Herglotz type and Noether's theorem for a time-delayed Hamiltonian system are studied. Firstly, the variational problem of Herglotz type with time delay in phase space is proposed, and the Hamilton canonical equations with time delay based on the Herglotz variational problem are derived. Secondly, by using the relationship between the non-isochronal variation and the isochronal variation, two basic formulae of variation of the Hamilton–Herglotz action with time delay in phase space are derived. Thirdly, the definition and criterion of the Noether symmetry for the time-delayed Hamiltonian system are established and the corresponding Noether's theorem is presented and proved. The theorem we obtained contains Noether's theorem of a time-delayed Hamiltonian system based on the classical variational problem and Noether's theorem of a Hamiltonian system based on the variational problem of Herglotz type as its special cases. At the end of the paper, an example is given to illustrate the application of the results.
]]>2018-10-03T00:05:22-07:00info:doi/10.1098/rsos.180208hwp:master-id:royopensci;rsos.1802082018-10-03Physics510180208180208http://rsos.royalsocietypublishing.org/cgi/content/short/5/9/171668?rss=1
Since the presentation of the radiation model, much work has been done to compare its findings with those obtained from gravitational models. These comparisons always aim at measuring the accuracy with which the models reproduce the mobility described by origin–destination matrices. This has been done at different spatial scales using different datasets, and several versions of the models have been proposed to adjust to various spatial systems. However, the models, to our knowledge, have never been compared with respect to policy testing scenarios. For this reason, here we use the models to analyse the impact of the introduction of a new transportation network, a bus rapid transport system, in the city of Teresina in Brazil. We do this by measuring the estimated variation in the trip distribution, and formulate an accessibility to employment indicator for the different zones of the city. By comparing the results obtained with the two approaches, we are able to not only better assess the goodness of fit and the impact of this intervention, but also understand reasons for the systematic similarities and differences in their predictions.
]]>2018-09-12T00:05:21-07:00info:doi/10.1098/rsos.171668hwp:master-id:royopensci;rsos.1716682018-09-12Physics59171668171668http://rsos.royalsocietypublishing.org/cgi/content/short/5/9/180706?rss=1
It is theorized that a mutualistic ecosystem's resilience against perturbations (e.g. species extinction) is determined by a single macroscopic parameter (network resilience), calculable from the network. Given that such perturbations occur owing to environmental changes (e.g. climate change and human impact), it has been predicted that mutualistic ecosystems that exist despite extensive environmental changes exhibit higher network resilience; however, such a prediction has not been confirmed using real-world data. Thus, in this study, the effects of climate change velocity and human activities on mutualistic network resilience were investigated. A global dataset of plant–animal mutualistic networks was used, and spatial analysis was performed to examine the effects. Moreover, the potential confounding effects of network size, current climate and altitude were statistically controlled. It was demonstrated that mutualistic network resilience was globally influenced by warming velocity and human impact, in addition to current climate. Specifically, pollination network resilience increased in response to human impact, and seed-dispersal network resilience increased with warming velocity. The effect of environmental changes on network resilience for plants was remarkable. The results confirmed the prediction obtained based on the theory and imply that real-world mutualistic networks have a structure that increases ecosystem resilience against environmental changes. These findings will enhance the understanding of ecosystem resilience.
]]>2018-09-12T00:05:21-07:00info:doi/10.1098/rsos.180706hwp:master-id:royopensci;rsos.1807062018-09-12Physics59180706180706http://rsos.royalsocietypublishing.org/cgi/content/short/5/9/180381?rss=1
We empirically verify that the market capitalizations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values for the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simple proportional growth with birth and death model previously employed to describe the size distribution of firms, cities, webpages, etc. We empirically validate the model and its main predictions, in terms of proportional growth (Gibrat's Law) of the coins and tokens. Estimating the main parameters of the model, the theoretical predictions for the power-law exponents of coin and token distributions are in remarkable agreement with the empirical estimations, given the simplicity of the model. Our results clearly characterize coins as being ‘entrenched incumbents’ and tokens as an ‘explosive immature ecosystem’, largely due to massive and exuberant Initial Coin Offering activity in the token space. The theory predicts that the exponent for tokens should converge to 1 in the future, reflecting a more reasonable rate of new entrants associated with genuine technological innovations.
]]>2018-09-05T00:05:21-07:00info:doi/10.1098/rsos.180381hwp:master-id:royopensci;rsos.1803812018-09-05Physics59180381180381http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/172281?rss=1
The identification of relationships in complex networks is critical in a variety of scientific contexts. This includes the identification of globally central nodes and analysing the importance of pairwise relationships between nodes. In this paper, we consider the concept of topological proximity (or ‘closeness’) between nodes in a weighted network using the generalized Erdős numbers (GENs). This measure satisfies a number of desirable properties for networks with nodes that share a finite resource. These include: (i) real-valuedness, (ii) non-locality and (iii) asymmetry. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to new methods to measure centrality. We show that the square of the leading eigenvector of an importance matrix defined using the GENs is strongly correlated with well-known measures such as PageRank, and define a personalized measure of centrality that is also well correlated with other existing measures. The utility of this measure of topological proximity is demonstrated by showing the asymmetries in both the dynamics of random walks and the mean infection time in epidemic spreading are better predicted by the topological definition of closeness provided by the GENs than they are by other measures.
]]>2018-08-29T00:05:50-07:00info:doi/10.1098/rsos.172281hwp:master-id:royopensci;rsos.1722812018-08-29Physics58172281172281http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/180563?rss=1
Osteoporosis, characterized by increased fracture risk and bone fragility, impacts millions of adults worldwide, but effective, non-invasive and easily accessible diagnostic tests of the disease remain elusive. We present a magnetic resonance (MR) technique that overcomes the motion limitations of traditional MR imaging to acquire high-resolution frequency-domain data to characterize the texture of biological tissues. This technique does not involve obtaining full two-dimensional or three-dimensional images, but can probe scales down to the order of 40 μm and in particular uncover structural information in trabecular bone. Using micro-computed tomography data of vertebral trabecular bone, we computationally validate this MR technique by simulating MR measurements of a ‘ratio metric’ determined from a few k-space values corresponding to trabecular thickness and spacing. We train a support vector machine classifier on ratio metric values determined from healthy and simulated osteoporotic bone data, which we use to accurately classify osteoporotic bone.
]]>2018-08-29T00:05:51-07:00info:doi/10.1098/rsos.180563hwp:master-id:royopensci;rsos.1805632018-08-29Physics58180563180563http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/180577?rss=1
Little is known about the structural patterns and dynamics of the first global trading market (FGTM), which emerged during the sixteenth century as a result of the Iberian expansion, let alone how it compares to today's global financial markets. Here we build a representative network of the FGTM using information contained in 8725 (handwritten) Bills of Exchange from that time—which were (human) interpreted and digitalized into an online database. We show that the resulting temporal network exhibits a hierarchical, highly clustered and disassortative structure, with a power-law dependence on the connectivity that remains remarkably robust throughout the entire period investigated. Temporal analysis shows that, despite major turnovers in the number and nature of the links—suggesting fast adaptation in response to the geopolitical and financial turmoil experienced at the time—the overall characteristics of the FGTM remain robust and virtually unchanged. The methodology developed here demonstrates the possibility of building and analysing complex trading and finance networks originating from pre-statistical eras, enabling us to highlight the striking similarities between the structural patterns of financial networks separated by centuries in time.
]]>2018-08-22T00:05:50-07:00info:doi/10.1098/rsos.180577hwp:master-id:royopensci;rsos.1805772018-08-22Physics58180577180577http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/172238?rss=1
Graphene nanosheets (GNSs) were grown on a Si nanoporous pillar array (Si-NPA) via chemical vapour deposition, using a thin layer of pre-deposited Ni nanocrystallites as catalyst. GNSs were determined to be of high quality and good dispersivity, with a typical diameter size of 15 x 8 nm. Light absorption measurements showed that GNSs had an absorption band edge at 3.3 eV. They also showed sharp and regular excitonic emitting peaks in the ultraviolet and visible region (2.06–3.6 eV). Moreover, phonon replicas with long-term stability appeared with the excitonic peaks at room temperature. Temperature-dependent photoluminescence from the GNSs revealed that the excitonic emission derived from free and bound excitonic recombination. A physical model based on band energy theory was constructed to analyse the carrier transport of GNSs. The Ni nanocrystallites on Si-NPA, which acted as a metal-enhanced fluorescence substrate, were supposed to accelerate the excitonic recombination of GNSs and enhanced the measured emission intensity. Results of this study would be valuable in determining the luminescence mechanism of GNSs and could be applied in real-world optoelectronic devices.
]]>2018-08-15T00:55:35-07:00info:doi/10.1098/rsos.172238hwp:master-id:royopensci;rsos.1722382018-08-15Physics58172238172238http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/180629?rss=1
Heteroepitaxial growth of aluminum nitride (AIN) has been explored by experiments, but the corresponding growth mechanism is still unrevealed. Here, we use molecular dynamics simulations to study effects of temperature and N : Al flux ratio on deposited AlN. When the temperature increases from 1000 K to 2000 K with an N : Al flux ratio of 2.0, the growth rate of the AlN film decreases. The crystallinity of the deposited AlN is distinctly improved as the temperature increases from 1000 K to 1800 K and it becomes saturated between 1800 K and 2000 K. The crystallinity of the deposited film at 1800 K increases with an increase in the N : Al flux ratio from 0.8 to 2.4, and this degraded a little at an N : Al flux ratio of 2.8. In addition, stoichiometry is closely related to crystallinity of deposited films. Film with good crystallinity is connected with a near 50% N fraction. Furthermore, the average mean biaxial stress and mean normal stress at 1800 K with N : Al flux ratios of 2.0, 2.4 and 2.8 are calculated, indicating that the deposited film with lowest stress has the best crystal quality and the defects appear where stresses occur.
]]>2018-08-15T00:55:35-07:00info:doi/10.1098/rsos.180629hwp:master-id:royopensci;rsos.1806292018-08-15Physics58180629180629http://rsos.royalsocietypublishing.org/cgi/content/short/5/8/171935?rss=1
Multiple countries have recently experienced extreme political polarization, which, in some cases, led to escalation of hate crime, violence and political instability. Besides the much discussed presidential elections in the USA and France, Britain's Brexit vote and Turkish constitutional referendum showed signs of extreme polarization. Among the countries affected, Ukraine faced some of the gravest consequences. In an attempt to understand the mechanisms of these phenomena, we here combine social media analysis with agent-based modelling of opinion dynamics, targeting Ukraine's crisis of 2014. We use Twitter data to quantify changes in the opinion divide and parametrize an extended bounded confidence XY model, which provides a spatio-temporal description of the polarization dynamics. We demonstrate that the level of emotional intensity is a major driving force for polarization that can lead to a spontaneous onset of collective behaviour at a certain degree of homophily and conformity. We find that the critical level of emotional intensity corresponds to a polarization transition, marked by a sudden increase in the degree of involvement and in the opinion bimodality.
]]>2018-08-01T00:05:39-07:00info:doi/10.1098/rsos.171935hwp:master-id:royopensci;rsos.1719352018-08-01Physics58171935171935